Dynamics of a piecewise-linear resonant circuit

The qualitative nature of the time evolution in a piecewiselinear lossy resonant circuit driven by a sinusoidal voltage source is investigated by computer-aided analysis using exact analytical formulas. A surprising wealth of different nonlinear phenomena is discovered. They are: stable and unstable harmonics, subharmonics, and even apparently completely disordered aperiodic "chaotic" motions. In the latter case, the hyperbolicity, strange attractor, and broad-band frequency spectrum normally associated with chaotic motions have all been observed using nearly exact piecewise-linear solutions. These results represent the most reliable numerical confirmation to date of chaotic motions in a real physical circuit.